document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=875187>Question 875187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sin(90-x)tan(360-x) divide by Cos(180-x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #528189 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=528189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin(90-x) = cos(x)<BR>\n" );
document.write( "cos(180-x) = -cos(x)<BR>\n" );
document.write( "tan(360-x) = -tan(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use these basic formulas to get your simplified expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start with:<BR>\n" );
document.write( "Sin(90-x)tan(360-x)/Cos(180-x)<BR>\n" );
document.write( "Replace sin(90-x) with cos(x)<BR>\n" );
document.write( "Replace cos(180-x) with -cos(x)<BR>\n" );
document.write( "Replace tan(360-x) with -tan(x)<BR>\n" );
document.write( "You get:<BR>\n" );
document.write( "cos(x)*-tan(x)/-cos(x)<BR>\n" );
document.write( "cos(x)/-cos(x) = -1<BR>\n" );
document.write( "Expression becomes:<BR>\n" );
document.write( "-1*-tan(x)<BR>\n" );
document.write( "-1*-1 = 1<BR>\n" );
document.write( "Expression becomes:<BR>\n" );
document.write( "tan(x)<BR>\n" );
document.write( "That's your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sin(90-x)tan(360-x)/Cos(180-x) = tan(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take any angle and replace x with it and you'll see that the equivalency is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example:<BR>\n" );
document.write( "x = 60 degrees (chosen at random)<BR>\n" );
document.write( "sin(90-x) = sin(90-60) = sin(30) in quadrant 1 = .5<BR>\n" );
document.write( "cos(180-x) = cos(180-60) = cos(120)= cos(60) in quadrant 2 = -.5<BR>\n" );
document.write( "tan(360-x) = tan(360-60) = tan(300) = tan(60) in quadrant 4 = -1.73205<BR>\n" );
document.write( "sin(90-x)*tan(360-x)/cos(180-x) = .5*-1.73205/-.5 = 1.73205<BR>\n" );
document.write( "tan(60) = 1.73205<BR>\n" );
document.write( "Answers are the same, therefore:<BR>\n" );
document.write( "sin(90-x)*tan(360-x)/cos(180-x) = tan(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The reference angle for all of the angles greater than 90 degrees is equal to 60 degrees.<BR>\n" );
document.write( "cos(120) = cos(180-60) therefore 60 is the reference angle in quadrant 2.<BR>\n" );
document.write( "tan(300) = tan(360-60) therefore 60 is the reference angle in quadrant 4.<BR>\n" );
document.write( "for the angle less than 90 degrees, the standard right triangle shows that:<BR>\n" );
document.write( "sin(90 - 60) = sin(30) = .5 = cos(90 - 30) = cos(60) = .5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the different quadrants, the relationships are shown in the following diagram:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/may1901.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A good reference that talks about reference angles can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php\" target = \"_blank\">http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php</a>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );